Challenge Level

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Challenge Level

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Challenge Level

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

Challenge Level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Challenge Level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Challenge Level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

Challenge Level

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Challenge Level

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Challenge Level

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Challenge Level

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Challenge Level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Challenge Level

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Challenge Level

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Challenge Level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Challenge Level

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Challenge Level

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Challenge Level

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Challenge Level

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Challenge Level

Can you mark 4 points on a flat surface so that there are only two different distances between them?

Challenge Level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Challenge Level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Challenge Level

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Challenge Level

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Challenge Level

Can you fit the tangram pieces into the outlines of the convex shapes?

Challenge Level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Challenge Level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Challenge Level

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Challenge Level

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Challenge Level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Challenge Level

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Challenge Level

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Challenge Level

Can you fit the tangram pieces into the outline of the plaque design?

Challenge Level

Can you fit the tangram pieces into the silhouette of the junk?

Challenge Level

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

Challenge Level

Can you fit the tangram pieces into the outline of the playing piece?

Challenge Level

Can you fit the tangram pieces into the outline of the clock?

Challenge Level

Can you fit the tangram pieces into the outline of Granma T?

Challenge Level

Can you fit the tangram pieces into the outlines of the rabbits?